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DUE  AS  STAMPED  BELOW 


FEB  2  0  2001 


12,000(11/95) 


FORM  NO.  DD6 


BERKELEY,  CA  94720 


^PUZZLES  TO  TEACH  GEOMETRY. 

IN  SEVENTEEN  CARDS,   NUMBERED  FROM  THE  FIRST  TO  THE  SEVENTEENTH  INCLUSIVE. 

We  have  here  given  two  hundred  and  four  combinations  of  three  isosceles  right  tri- 
angles ;    a  simpler  form  of  the  Chinese  tangram. 

The  value  of  these  puzzles,  in  cultivating  a  geometrical  taste  and  ability,  has  been 
acknowledged  since  the  time  of  Archimedes,  who  is  said  to  have  invented  a  similar 
play;    the  Chinese  tangram  is,  however,  too  difficult  to  interest  beginners. 

The  present  series  of  cards  is  intended  chiefly  for  our  common  schools,  as  a  more 
natural  introduction  to  science  than  the  abstract  language  of  arithmetic.  They  are 
accompanied  by  triangular  blocks  of  two  sizes,  from  three  of  which,  selected  according 
to  the  line  at  the  foot  of  the  card,  any  of  the  combinations  can  be  made. 

The  teacher  may  either  introduce  them  as  a  regular  exercise  of  the  school,  or  use  them  as  rewards  of  merit, 
—  allowing  those  whose  conduct  deserves  it  to  play  with  a  card  and  three  triangles.  Questions  may  be  asked, 
when  the  teacher  has  time  and  opportunity ;  —  such  as.  How  many  corners,  or  angles,  has  this  figure  ?  Which 
of  them  are  square,  or  right  angles  ?  Which  acute  ?  What  part  of  a  right  angle  is  the  acute  angle  ?  Which 
angles  are  obtuse  ?  How  many  of  the  acute  equal  one  obtuse  >  Which  angles  are  concave,  or  ipdent  the 
figure  }  To  how  many  of  the  acute  angles  is  this  concave  angle  equal,  measured  on  the  outside  ?  On  the  in- 
side ?  How  many  diagonals  can  be  drawn,  or  straight  lines  through  the  figure,  from  corner  to  corner  ?  Which 
diagonal  will  divide  the  figure  in  equal  halves  ?  Will  any  line  divide  the  figure  in  equal  parts  ?  that  is,  is  it 
symmetrical  ?  Will  either  of  two  or  more  lines  ?  that  is,  is  the  figure  symmetrical  on  more  than  one  axis  }  If 
the  figure  has  concave  angles,  lines  can  be  drawn  outside  the  figure,  from  corner  to  corner,  or  catagonals. 
How  many  catagonals  can  be  drawn  in  this  figure  }  Will  a  line  perpendicular  to  any  point  in  the  catagonal  be 
an  axis  of  symmetry .?  If  so,  at  what  point  >  Is  there  more  than  one  way  of  forming  this  figure,  with  the 
same  triangles  }  Can  you  form,  with  the  same  triangles,  a  figure  like  this,  except  that  the  left  side  shall  answer 
to  the  right  of  this,  and  the  right  to  the  left,  or  the  top  to  the  bottom,  and  the  bottom  to  the  top  ?  &c.,  &c.,  (fee. 

The  following  are  from  gentlemen  who  have  seen  the  manuscript. 

From  Benjamik  Peikce,  Perkins  Professor  of  Astronomy  and  Mathematics  in  Harvard  University. 

"  My  dear  Sir  •  —  I  am  quite  pleased  with  your  design  of  introducing  the  principle  of  the  Chinese  puzzle  into  the  elementary 

schools,  as  a  method  of  instructing  young  children  in  the  practical  analysis  of  forms.     This  puzzle  has  always  seemed  to  me  to  be 

worth  more  than  a  mere  amusement,  and  to  be  of  considerable  intellectual  value  in  the  development  of  geometrical  ideas. 

"  Very  sincerely  and  faithfully  your  friend, 

"Benjamin  Peirce." 

From  Thomas  Shebwin,  Principal  of  the  English  High  School,  Boston. 
"  I  have  just  examined  Rev.  Mr.  Hill's  plates  for  geometry  for  alphabet  schools,  and  I  think  that  his  plan  will  be  productive  of 
valuable  instruction,  as  well  as  much  harmless  amusement. 

"Thomas  Sherwin." 

The  Puzzle  has  been  introduced,  by  blackboard,  into  the  Alphabet  School  of  District  No.  IV.,  Waltham,  and 
is  highly  prized  by  the  teacher,  a  pupil  of  the  Normal  School,  greatly  esteemed  wherever  she  has  taught.  It 
has  also  been  approved  by  every  teacher  to  whom  the  manuscript  has  been  shown. 

PUBLISHED   BY  WM.  CROSBY   AND   H.  P.  NICHOLS,  111   WASHINGTON   STREET,   BOSTON. 

Entered  according  to  Act  of  Congress,  in  the  year  1843,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


r.  ..\ . 


CAJORI 


PUZZLES  TO  TEACH  GEOMETRY. 
First   Card. 


H5. 


Two  Triangles  of  equal  size. 

Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Cleric's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 

T     ivi330ftl3 


H 


"^ 


PUZZLES  TO  TEACH  GEOMETRY. 
Second   Card* 


Three  Triangles  of  equal  size. 

Entered  according  to  Act  of  Congroas,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 
Third   Card. 


Three  Triangles  of   equal  size. 


Entered  according  to  Act  of  Congreas,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


u 


r 


PUZZLES  TO  TEACH  GEOMETRY. 
Fourth   Card* 


Three  Triangles  of   equal  size. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


HS 


PUZZLES  TO  TEACH  GEOMETRY. 
Fifth   Card. 


/V 


"\ 


** 


z 


A 


X 


One  large  and  two  small  Triangles. 

Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerii's  Office  of  the  District  Court  of  the  District  of  Massachuseiia 


U  A 


ft  5- 


PUZZLES  TO  TEACH  GEOMETRY. 
8ixth   Card* 


One  large  and  two  small  Triangles. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


H^ 


PUZZLES  TO  TEACH  GEOMETRY. 
Seventh   Card. 


V^ 


One  large  and  two  small  Triangles. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk'a  Office  of  the  District  Court  of  the  District  of  Maasachuaetta. 


ah 


i  I 


PUZZLES  TO  TEACH  GEOMETRY. 
Eigrhth  Card. 


Z 


One  large  and  two  small  Triangles. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


/    \      i    ^     / 


14^ 


PUZZLES  TO  TEACH  GEOMETRY. 
Ninth   Card. 


One  large  and  two  small  Triangles- 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk'a  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


H-S 


PUZZLES  TO  TEACH  GEOMETRY. 
Tenth   Card. 


Two  large  and  one  small  Triangle. 


Enteied  according  lo  Act  of  Congreas,  in  the  year  1848,  by  T.  Hill,  in  ihe  Clerk's  Office  of  ihe  District  Court  Oi   he  .  istrict  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 


EleTenth 


Card. 

-> 


.A 


X 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Maasachuseits. 


PUZZLES  TO  TEACH  GEOMETRY. 
Twelftb   Card. 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 
Thirteenthi    Card* 


Two  large  and  one  small  Triangle. 

Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  liie  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 
Fourteenth    Card. 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congress,  in  the  year  1S18,  by  T.  Hill,  in  the  Clerk's  Office  of  tlie  District  Court  of  tlie  District  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 
Fifteenth   Card. 


N. 


X 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congresa,  in  the  year  1848,  by  T.  Hill,  in  the  tlerli's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


PUZZLES  TO  TEACH  GEOMETRY. 
Sixteenth   Card. 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  HaL,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


a 


H-r- 


PUZZLES  TO  TEACH  GEOMETRY. 
Seventeenth   Card* 


Two  large  and  one  small  Triangle. 


Entered  according  to  Act  of  Congress,  in  the  year  1848,  by  T.  Hill,  in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


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